Warm-up 3-25
1. Factor out the GCF of
the following Polynomial
4𝑥3𝑦4 – 8𝑥5𝑦6 + 2𝑥2𝑦10
Factor the trinomials
4. 𝑥 2 + 8𝑥 + 12
7. 6𝑥 2 + 59𝑥 − 10
Multiply the polynomials using FOIL.
2. (2𝑥 − 1)(𝑥 + 5) 3. (𝑥 + 4)(𝑥 − 4)
6. 4𝑥 2 − 32𝑥 − 80
5. 𝑥 2 − 9𝑥 + 20
8. 6𝑥 2 + 31𝑥 + 35
Factor the binomial
9. 4𝑥 2 − 25
Factoring when Leading
Coefficient is greater than 1
Essential Question: How do you
factor when the leading coefficient is
greater than 1
Key words/definitions
• Leading Coefficient-number in front of the
variable with the degree (highest exponent)
• Constant-number not connected to a variable
• Factor by grouping- grouping terms with
common factors and then factoring out a GCF
Process
**Make sure equation is in standard form**
For an equation with a leading coefficient greater
than 1:
1. Multiply the leading coefficient by the constant
2. Find two numbers that multiply to that number
and add up to the middle term
3. Write out the entire polynomial, splitting the
middle term into two separate terms
4. Factor by grouping
Practice as a Class!
• Example 1: 2x2 + 11x +5
Leading
Coefficient
Factor by
Grouping
Constant
5 * 2 = 10
What multiplies to 10 and adds to 11?
10 and 1!!
2x2 + 10x + 1x +5
(2x2 + 10x) + (1x +5)
GCF of (2x2 + 10x) is 2x so we factor out a 2x
GCF of (1x + 5) is 1 so we factor out a 1
2x(x+5) + 1(x + 5)
Answer: (2x+1) (x+5)
Practice as a Class!
• Example 2: 3x2 - 4x - 7
Leading
Coefficient
Factor by
Grouping
Constant
3 * -7 = -21
What multiplies to -21 and adds to -4?
-7 and 3!!
3x2 – 7x + 3x -7
(3x2 - 7x) + (3x - 7)
GCF of (3x2 - 7x) is x so we factor out an x
GCF of (3x - 7) is 1 so we factor out a 1
x(3x - 7) + 1(3x - 7)
Answer: (2x+1) (x+5)
Practice as a Class!
• Example 3: 4x2 + 10x + 4
Leading
Coefficient
Factor by
Grouping
Constant
4 * 4 = 16
What multiplies to 16 and adds to 10?
8 and 2!!
4x2 + 8x + 2x + 4
(4x2 + 8x) + (2x + 4)
GCF of (4x2 + 8x) is 4x so we factor out a 4x
GCF of (2x + 4) is 2 so we factor out a 2
4x(x + 2) + 2(x + 2)
Answer: (4x+2) (x+2)
What if you have a negative
leading coefficient?
• If you have a negative leading coefficient,
factor a -1 out of the ENTIRE polynomial and
then factor normally.
• Make sure to bring the -1 down to your
answer!
• Example -3x2 - 4x – 7 = -1(3x2 + 4x + 7)
= -1(2x+1) (x+5)
Practice on your Own!
1. 3x2 + 5x + 2
2. 2x2 + 21x – 11
• 3. 6x2 – 19x + 15
4. -8x2 + 14x + 15